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X(6), X(99), X(187) points at infinity of ABC sidelines 

Given an isoconjugation with pole W(p : q : r), the locus of point P such that the pedal triangles of P and its Wisoconjugate P* are parallelogic is the cubic nK0(W, X6). See CL022. This cubic is a nK+ if and only if W lies on K150. K150 is a nonpivotal isocubic with pole X(14567) = [ a^4 (b^2 + c^2  2a^2) : ... : ... ] = X6 x X187 = X32 x X524 and root G. It has three real asymptotes parallel to the sidelines of ABC. Kjp = K024 is the most interesting example with W = X(6). K151 is another example of such nK0+(W, X3) with W = X(99) (Steiner point). 
